Preparation for the energy of language

Preparation for the energy of language

TANAKA Akio

The energy of language seems to be one of the most fundamental theme for the further step-up  study on language at the present for me. But the theme was hard to put on the mathematical description. Now I present some preparatory  papers written so far.

1. Potential of Language / Floer Homology Language / 16 June 2009
2. Homology structure of Word / Floer Homology Language / Tokyo June 16, 2009
3. Amplitude of meaning minimum / Complex Manifold Deformation Theory / 17 December 2008
4. Time of Word / Complex Manifold Deformation Theory / 23 December 2008

Tokyo
3 April 2015
Sekinan Library

The Days of von Neumann Algebra

The Days of von Neumann Algebra 

viz. The cited papers' texts are shown at the blog site SRFL News' January 2015 blogs.

TANAKA Akio

1.
My study's turning point from intuitive essay to mathematical writing was at the days of learning von Neumann Algebra, that was written by four parts from von Neumann Algebra 1 to von Neumann Algebra 4. The days are about between 2006 and 2008, when I was thinking about switching over from intuitive to algebraic writing. The remarkable results of writing these papers were what the relation between infinity and finiteness in language was first able to clearly describe. Two papers of von Neumann 2. Property Infinite and Purely Infinite, were the trial to the hard theme of infinity in language.The contents' titles are the following.

von Neumann Algebra 
On Infinity of Language
1 von Neumann Algebra 1
2 von Neumann Algebra 2
3 von Neumann Algebra 3
4 von Neumann Algebra 4
References
1 Algebraic Linguistics 
2 Distance Theory Algebraically Supplemented
3 Noncommutative Distance Theory
4 Clifford Algebra
5 Kac-Moody Lie Algebra
6 Operator Algebra

..................................................................................................................................

2.
The papers of von Neumann Algebra and References are the next.

von Neumann Algebra 1 
1 Measure
2 Tensor Product
3 Compact Operator

von Neumann Algebra 2
1 Generation Theorem

von Neumann Algebra 3
1 Properly Infinite
2 Purely Infinite

von Neumann Algebra 4
1 Tomita's Fundamental Theorem
2 Borchers' Theorem

Algebraic Linguistics <Being grateful to the mathematical pioneers>
On language universals, group theory is considered to be hopeful by its conciseness of expression. Especially the way from commutative ring to scheme theory is helpful to resolve the problems a step or two.
1 Linguistic Premise
2 Linguistic Note
3 Linguistic Conjecture
4 Linguistic Focus
5 Linguistic Result 

Distance Theory Algebraically Supplemented
Algebraic Note
1 Ring
2 Polydisk <Bridge between Ring and Brane>
3 Homology Group
4 Algebraic cycle
Preparatory Consideration
1 Distance
2 Space <9th For KARCEVSKIJ Sergej>
3 Point
Brane Simplified Model
1 Bend
2 Distance <Direct Succession of Distance Theory>
3 S3 and Hoph Map 

Noncommutative Distance Theory
Note
1 Groupoid
2 C*-Algebra
3 Point Space
4 Atiyah’s Axiomatic System
5 Kontsevich Invariant
[References]
Conjecture and Result
1 Sentence versus Word 
2 Deep Fissure between Word and Sentence

Clifford Algebra
Note
1 From Super Space to Quantization
2 Anti-automorphism
3 Anti-self-dual Form
4 Dirac Operator
5 TOMONAGA's Super Multi-time Theory
6 Periodicity
7 Creation Operator and Annihilation Operator
Conjecture
1 Meaning Product 

Kac-Moody Lie Algebra 
Note
1 Kac-Moody Lie Algebra
2 Quantum Group
Conjecture
1 Finiteness in Infinity on Language

Operator Algebra 
Note
1 Differential Operator and Symbol
2 <A skipped umber>
3 Self-adjoint and Symmetry
4 Frame Operator
Conjecture
1 Order of Word
2 Grammar3 Recognition

....................................................................................................................................

3.
After writing von Neumann Algebra 1 - 4,  I successively wrote the next.

Functional Analysis
Reversion Analysis Theory
Holomorphic Meaning Theory
Stochastic Meaning Theory

Especially Stochastic Meaning Theory clearly showed me the relationship between mathematics and physics, for example Brownian motion in language. After this theory I really entered the algebraic geometrical writing by Complex manifold deformation Theory. The papers are shown at Zoho site's sekinanlogos.

• sekinanlogos
  

Complex Manifold Deformation Theory

• Distance of Word
  
• Reflection of Word
  
• Uniqueness of Word
  
• Amplitude of Meaning Minimum 
  
• Time of Word
  
• Orbit of Word
  
• Understandability of Language    
  
• Topological Group Language Theory
  
• Boundary of Words
  

Symplectic Language

• Symplectic Topological Existence Theorem
  
• Gromov-Witten Invariantational Curve
  
• Mirror Symmetry Conjecture on Rational Curve   ​
  
• Isomorphism of Map Sequence 
  
• Homological Mirror Symmetry Conjecture by KONTSEVICH
  
• Structure of Meaning
  

Floer Homology Language

• Potential of Language      
  
• Supersymmetric Harmonic Oscillator
  
• Grothendieck Group   ​
  
• Reversibility of language
  
• Homology Generation of Language
  
• Homology Structure of word
  
• Quantization of Language
  
• Discreteness of Language
  

.....................................................................................................................................

4.
The learning from von Neumann Algebra 1 ended for a while at Floer Homology Language,  where I first got trial papers on language's quantisation or discreteness. The next step was a little apart from von Neumann algebra or one more development of algebra viz. arithmetic geometry.

#   Here ends the paper.
## The cited papers' texts are also shown at this site.

vide: The days between von Neumann Algebra and Complex Manifold Deformation Theory

Tokyo
3 December 2015
SIL

The days between von Neumann Algebra and Complex Manifold Deformation Theory

The days between von Neumann Algebra and Complex Manifold Deformation Theory

vide:  Applied papers with this essay are reprinted at SRFL News' January 2015 blogs.

TANAKA Akio

von Neumann Algebra was written from 3 April 2008 to 2 May 2008. And Complex Manifold Deformation Theory was written from 30 November 2008 to 9 January 2009. In the days between the two theories I wrote the following 4 paper groups.

Functional Analysis 

Reversion Analysis Theory

Holomorphic Meaning Theory

Stochastic Meaning Theory

These days were the preparatory time for regularised writing by algebraic geometry at Zoho site. But they were relatively precious days for thinking about the reshuffling mathematics and physics related with language. Especially Stochastic Meaning Theory was a milestone for mathematical approaching to physical phenomenon of language.Stochastic Meaning Theory's titles are the next.

Stochastic Meaning Theory

• Period of Meaning
• Period of Meaning 2 
• Place of Meaning 
• Energy of Language 
• Language as Brown Motion 

On the other hand, I really realised that mathematical writing of  natural phenomenon, for example natural language, inevitably needed clear routes by mathematics that was represented by function analysis approach. Functional Analysis and Reversion Analysis Theory were the trial papers aiming for new ground, especially the comparison of finiteness and infinity in generation of words and sentences. 

Functional Analysis 1

Note

1. Baire's Category Theorem

2. Equality and Inequality

3. Space4. Functional

Conjecture

1. Finiteness of Vocabulary

2. Distance at Hypersurface

Functional Analysis 2

Note

1. Pre-Hilbert Space and Hilbert Space

2. Orthogonal Decomposition

Conjecture

1. Generation of Word

Reversion Analysis Theory

1. Reversion Analysis Theory

2. Reversion Analysis Theory 2

But at that time I could not decide the main field of mathematics for applying to language study. Moreover I never thought about language models parting from natural language and constructing the new field for thinking about language universals. After these preparation of algebra that was started from Premise of Algebraic Linguistics 1 -1 at 11 September 2007, I barely reached to the entrance of algebraic geometry's use for language and making the language models. It was Complex Manifold Deformation Theory which began to write at 30 November 2008 titling Distance of Word,  one of my main themes for language universals from the very starting of language study. Thus my study first focused to making language models of algebraic geometry using complex manifold.

Complex Manifold Deformation Theory

• Distance of Word
• Reflection of Word 
• Uniqueness of Word
• Amplitude of Meaning Minimum  
• Time of Word
• Orbit of Word 
• Understandability of Language 

# Here ends the paper.

Tokyo

6 January 2015

SIL

What facts does Three Conjectures for Dimension, Synthesis and Reversion show us?

What facts does Three Conjectures for Dimension, Synthesis and Reversion show us?

TANAKA Akio

1.
True-false problem of the Crete gives us the infinite circulation of true-false value.
This fact indicates us the existence of deep structure or hierarchy in language.
The Crete's true-false is solved by the perspective from 2-dimension to 3-dimension on structure in language world.

2.
Language has long history as the system of etymology. Apparently language has gradually added the  new meaning on the old established meaning in word. At this point new meaning is synthesised to the old meaning. At synthesis word mathematically reduces its dimension to the lower one. As the result time in word relatively occurred in the new word and inevitably connected with  dimension.

3.
Where and how does word exists in the world?
The distance from a certain point is absolutely demanded for measuring or observing for knowing the word's place. Reversion is a result for measuring or observing from a point.

4.
For precise description of dimension, synthesis and reversion mathematical tools are definitely needed and for more simple describing algebraic method is the most useful to approach for me and in order to easy-seeing and clear intuition geometrical approach is always inevitable to searching. I am greatly thanks to relevant mathematicians researching against severe problems still now for contemporary times.

Kodaira, Tokyo
20 November 2014
SIL

Conjecture for reversion of language

Conjecture for reversion of language

TANAKA Akio

Conjecture for reversion of language
14/10/2013 11:21
Conjecture for reversion of language
Language has a standstill point in itself.

[Explanation]
This conjecture’s intuition is prepared at the paper, Reversion Theory 2004 at Sekinan Research Field of Language.
This conjecture’s mathematical basis is given by Kato conjecture 1986. The conjecture is said to be given cohomological Hasse principle at unramified number theory.

[References]
News. hillssouthroad
News
Reversion Theory 2004
14/10/2013 11:10
Kato conjecture 1986 
13/10/2013 23:07
K. KATO, 1986 
12/10/2013 19:52
Read more: http://hillssouthroad.webnode.com/

Tokyo
1 May 2014
Sekinan Research Field of Language

Reversion Conjecture Revised

Reversion Conjecture Revised

TANAKA Akio 
                                      
Conjecture for reversion of language

14/10/2013 11:21
Conjecture for reversion of language
Language has a standstill point in itself.

[Explanation]
This conjecture’s intuition is prepared at the paper, Reversion Theory 2004 at Sekinan Research Field of Language.
This conjecture’s mathematical basis is given by Kato conjecture 1986. The conjecture is said to be given cohomological Hasse principle at unramified number theory.

[References]
News. hillssouthroad
News
Reversion Theory 2004
14/10/2013 11:10
Kato conjecture 1986
13/10/2013 23:07
K. KATO, 1986
12/10/2013 19:52
Read more: http://hillssouthroad.webnode.com/

                                       Tokyo
                                 1 May 2014
                Sekinan Research Field of Language

------------------------------------------------------------------------------------
New starting point on language, Reversion conjecture
Reversion conjecture may become the new starting point on language,
especially on language universals.
Reversion conjecture has the preparatory thinking by algebraic geometry.
Refer to the next.
Dimension Decrease Conjecture 2013 
Synthesis Conjecture 2013
Reversion Conjecture 2013

                                              Tokyo
                                        20 May 2014
                     Sekinan Research Field of Language

---------------------------------------------------------------------------------------------------------

Interpretation of Reversion conjecture
According to Reversion conjecture, language has a standstill point in itself.
Here it means that every word has standstill point and every word has a
proper distance from the standstill point. This distance constructs word'
proper meaning and grammar.

Refer to the next.
Distance Theory 2004 / SRFL
Reversion Theory 2004 / SRFL

                                             Tokyo
                                        20 May 2014
                     Sekinan Research Field of Language

---------------------------------------------------------------------------------------------------------


Simplification of Reversion conjecture
Reversion conjecture is simplified by Kerz-Saito's theorem, 2012.

Kerz, M., Saito, S.: Cohomological Hasse principle and
motivic cohomology of arithmetic schemes. 2012

                                             Tokyo
                                        20 May 2014
                     Sekinan Research Field of Language

Conjecture for synthesis of meaning in word

Conjecture for synthesis of meaning in word

TANAKA Akio

Synthesis
1 Conjecture for synthesis of meaning in word
29/09/2013 19:25
For synthesis of meaning in word, Conjecture: Condition for synthesis of meaning in word is proposed by cohomological expression.

2 Conjecture: Condition for synthesis of meaning in word
29/09/2013 18:38
On condition for synthesis of meaning in word,  at conjecture is proposed  by the next result of etale cohomology.
Result
——————————————————-
Canonical natural equivalence
The next two are left exact additional functors.
F: A  -> A’ 
G: A’ -> A”
A and A’ have enough many injective objects.
If F transfers A’ s injective object to G acyclic object, the next canonical natural equivalence is concluded.
R ( G O F ) =~ RG O RF.
——————————————————–
Conjecture
Preparation
Word is shown by R. This word is called old word.
Base meaning in word is shown by F.
Word that has base meaning is shown by RF.
Additional meaning to word is shown by G.
Word that has additional meaning is shown by RG. This word is called intermediate word.
Word that has base meaning and additional meaning is shown by R ( G O F ). This word is called new word.
Conjecture
For completion of new word, old word and intermediate word have the condition shown by the canonical natural equivalence of etale cohomology.

3 Canonical natural equivalence
29/09/2013 18:08
Canonical natural equivalence
The next two are left exact additional functors.
F: A  -> A’ 
G: A’ -> A”
A and A’ have enough many injective objects.
If F transfers A‘s injective object to G acyclic object, the next canonical natural equivalence is concluded.
R ( G O F ) =~ RG O RF.

Dimension Decrease Conjecture

Dimension Decrease Conjecture

TANAKA Akio

1 Dimension conjecture of word
23/09/2013 23:04
Word has dimension. New addition of meaning to word makes dimension of word decrease.
Basis
Pull back map of higher Chow group
23/09/2013 16:11
Pull-back map of higher Chow group is bijection.
Conjecture on language
When word has additional meaning, dimension of word is decreased by dimension of additional  meaning.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho.

2 SAITO Shuji, SATO Kanetomo
24/09/2013 10:14S
SAITO Shuji, SATO Kanetomo. Algebraic Cycle and Etal Cohomology. 2012.

3 Pull-back map of higher Chow group
23/09/2013 16:11
Pull-back map of higher Chow group is bijection.
Conjecture on language
When word has additional meaning, dimension of word is decreased by dimension of additional meaning.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho.

4 Y. Nesterenko, A. Suslin
23/09/2013 15:30
Y. Nesterenko, A. Suslin.
Homology of the general linear group over a local ring, and Milnor’s K-theory. Math. 1990.

5 Higher Chow ring
23/09/2013 15:21
Double graded Abel group becomes double graded ring by defined intersection product.
Its product become commutative at one degree and become noncommutative at the another degree.

6 W.Fulton
23/09/2013 11:01
W. Fulton. Intersection Theory, 2nd ed. 1988.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho.

7 V. Vodoedsky
22/09/2013 20:09V.
V. Vodoedsky
On motivic cohomology with Z/2-coefficients. Math.98. 2003.
On motivic cohomology with Z/l-coefficients. Ann. of Math.

8 Map that norm residue map induces
22/09/2013 20:03
When k is field and n is commutative integer, map that norm residue map induces is bijection.

Paper for Dimension

Paper for Dimension


1. Dimension Decrease Conjecture
2. Conjecture for synthesis of meaning in word
3. Reversion Conjecture Revised 
    Proto 3. Conjecture for reversion of language

Tokyo

14 June 2015

Sekinan Paper

Sekinan Paper

Sekinan Paper

Tokyo

1 June 2015 arranged

Study result of Sekinan Library from 1986, SRFL from 2003 and Zoho from 2008

Sekinan Paper is the paper site of Sekinan Library and SRFL Sekinan Research Field of Language.
Sekinan Library was founded at Tachikawa, Tokyo in 1986 for the study of language. 
In 2003 for the special study site of language universals, SRFL Sekinan Research Field of Language was added at Hakuba, Nagano.  

Hydrangea

June 2015

At least three elements for language universals

At least three elements for language universals

TANAKA Akio

Supposition 1:
Three elements for language universals

For language universals, now I suppose at least three elements being  based from mathematical description.

Three elements for language universals are energy, dimension and distance.

The most fundamental element is energy. By this energy, all the movements and changes occur in language.
vide: 

• Edward Sapir, Language, 1921
• Substantiallity

All the languages are located at a certain dimension in space. By this dimension, confusions in language are averted.
vide:

• True-false problem of the Crete

In language, all the movements and changes inevitably make distance occurred. By this distance, important phases of language are clearly defined.
vide:

• Distance Theory 

...........................................................................................................................

Supposition 2:
Mathematical description for three elements of language universals

Energy, dimension and distance can be describe by mathematical writing.

Energy in language is now preparatory description til now.
vide:

• Energy of Language / Stochastic Meaning Theory
• Energy and Distance / Energy Distance Theory
• Energy and Functional / Energy Distance Theory
• Potential of Language / Floer Homology Language

For dimension, definite results are presented being aided by arithmetic geometry.
vide:

• Three Conjectures for Dimension, synthesis and Reversion with Root and Supplement

For distance, its vast and vagueness of the concept can not be grasped up. But related papers of mine are probably the most in number.
vide:

• Distance / Direct Succession of Distance Theory / Distance Theory Algebraically Supplemented
• Distance of Word / Complex Manifold Deformation Theory

............................................................................................................................

This paper is not finished.

Tokyo
27 February 2015
SIL